I usually don't bother answering a Gish Gallop, but...

1 - They didn't complete the study, it was only 13 people with an existing history of mental disorders

2 - They basically said it's so within the tolerances that it's probably just chance, and that regular soda did as bad or worse

3 - Could only get the abstract, and it says nothing about their findings

4 - Combines aspartame and acesulfame-K, so it's hard to tell from the abstract. The methodology doesn't fill me with a lot of hope for it though.

5 - Seems to be the same study as 4 (same group of French people, same author), but for cardiovascular disease instead of cancer? Which, yeah, fat people drink diet soda, have heart disease, and get cancer more than thin people. I'm not sold on their methodology

6 - It's a rat study. Again, I can't see anything but the abstract, so it's hard to say. But any study that doesn't do a comparative analysis against regular sugar is suspect in my book

7 - Like 2, this one says that it's probably just chance in the conclusion.

And look, if this was some new chemical on the block, maybe I'd agree that it should have some more testing. But it's aspartame. It's been being actively studied since 1965. It's had a lot of negative PR backed by Domino (et al), which has created a huge amount of public concern. And will all of that, the studies still come out a hundred to one that there's not really any link to anything.

Yes, you can find studies that say "aspartame scary." But they're basically like all the ones you linked above. Dubious. Most even admit they're dubious (as seen above). And almost none of the ones that push the "scary" rhetoric compare the effects against regular table sugar, which is also heavily linked to increased cancer/heart disease risk. So it's not even intellectually honest, even when their numbers happen to random out to slightly agreeing with them.